Considering the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(189, 1.91).
b) The probability that the average hand length is less than 191 is of 0.8531 = 85.31%.
c) The first quartile is of 187.7 mm.
d) The assumption is necessary, as the sample size is less than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. The mean is the same as the population mean.For sample size less than 30, such as in this problem, the assumption of normality is needed to apply the Central Limit Theorem.The parameters in this problem are given as follows:
[tex]\mu = 189, \sigma = 7.4, n = 15, s = \frac{7.4}{\sqrt{15}} = 1.91[/tex]
Hence the sampling distribution of sample means is classified as follows:
x¯ ~ N(189, 1.91).
The probability that the average hand length is less than 191 is the p-value of Z when X = 191, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (191 - 189)/1.91
Z = 1.05
Z = 1.05 has a p-value of 0.8531, which is the probability.
The first quartile of the distribution is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 189)/1.91
X - 189 = -0.675 x 1.91
X = 187.7 mm.
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A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]Find the surface area of a glazed donut with an outer diameter of 7 cm and an inner diameter of 3 cm. The donut is 2 cm tall
Solution:
If the outer diameter is 7, then the outer radius is b=7/2.
On the other hand, if the inner diameter is 3, then the inner radius is a= 3/2.
Now, the surface area of a torus (glazed donut) with inner radius a and outer radius b is given by
[tex]SA=\pi^2\mleft(b+a\mright)\mleft(b-a\mright)\text{ =}\pi^2(b^2-a^2)[/tex]Then, applying the data of the problem to the above equation, we can conclude that the surface area of the given glazed donut would be:
[tex]SA=\pi^2(b^2-a^2)=\pi^2((\frac{7}{2})^2-(\frac{3}{2})^2)=98.69[/tex]so that, the correct answer is:
[tex]SA=98.69\approx98.7[/tex]
a rectangle width is 3 1/2 inches and the lenght is 4 3/4 inches. What is the area of the rectangle?
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of the rectangle = [tex]4 \frac{3}{4}[/tex] inches
= 19 / 4 inches
The width of the rectangle = [tex]3 \frac{1}{2}[/tex] inches
= 7 / 2 inches.
Since, We know that;
The area of the rectangle = Length x Width
Substitute all the values , we get;
The area of the rectangle = Length x Width
The area of the rectangle = 19 / 4 x 7 / 2
= 133 / 8 inches²
= [tex]16 \frac{5}{8}[/tex] inches²
Therefore,
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
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What is 5 5/7 divided by 1 3/5 divided by 4 2/3 in simplest form?
The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].
What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.
Given that: (55/7)/(13/5)/(42/3)
First to simplify:
[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]
So, expression becomes,
[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]
Now to simplify this expression.
Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]
Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]
Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.
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Write the rate as fraction in simplest form 22 gallons of pest rifles for 8 acres of crops
Since the given rate is 22 gallons of pest for 8 acres of crops, then
We need to find how many acres per gallon
Then we will divide 22 acres by 8 gallons to find the rate
[tex]rate=\frac{22}{8}[/tex]Divide up and down by 2 to simplify
[tex]\begin{gathered} rate=\frac{\frac{22}{2}}{\frac{8}{2}} \\ \\ rate=\frac{11}{4} \end{gathered}[/tex]The answer is:
The rate is 11/4 gallon per acre (2 3/4)
Point B is on line segment AC. Given BC = 10 and AB = 5, determine the lengthAC.Answer: AC= Anyone know how to solve these???
3
1) Let's sketch that, to better understand this:
2) Considering the Segment Addition Postulate, we can write that:
DF = DE + EF Plug into that the given values
9 = 6 + EF
9-6 = 6-6 + EF
3 = EF
EF =3
3) Hence, the line segment EF is 3 units long
For each equation in the table, give the slope of the graph.
Solving the Question
Linear equations are typically organized like this: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
When the equation is like [tex]y=b[/tex], it means that it is a horizontal line and the slope is 0.
When the equation is like [tex]x=d[/tex], it is a vertical line and the slope is undefined.
AnswerFirst equation: 0
Second equation: undefined
Third equation: [tex]\dfrac{4}{5}[/tex]
Use the model to solve for x
PLS HELPPP
Answer:
I think x is -6
Step-by-step explanation:
Side 1:
3x+1
3x-10+1=(-29)
3x-6+1=(-17)
Side 2:
2x-5
2x-10-5=(-25)
2x-6-5=(-17)
A bag contains 5 red marbles and 3 blue marbles. A marble is selected at random and not replaced into the bag. Another marble is then selected from the bag. How would you describe these two events?
Marble Events
there are 5 + 3 = 8 marbles
If one marble is selected then there are now
8 - 1 = 7 marbles
Then answer is
The two events are Dependent
Event B is dependent on Event A
7. An antique dealer has a fund of $1,160 for investments. She spends 50%of the fund on a 1911 rocking chair. She then sells the chair for $710, all ofwhich she returns to the fund.a) What was the percent gain on the investment?b) What percent of the original value of the fund is the new value of the fund?
Given:
Total amount dealer has is $1160.
Spend 50% of the fund to buy a 1911 rocking chair and sells it for $710.
[tex]Fund\text{ she spends on chair=}1160\times\frac{50}{100}[/tex][tex]Fund\text{ she spends on chair= \$580}[/tex]a)
[tex]\text{Fund gain on selling the chair= 710-580}[/tex][tex]\text{Fund gain on selling the chair= \$}130[/tex][tex]\text{Percent gain on the investment=}\frac{130}{580}\times100[/tex][tex]\text{Percent gain on the investment=}22.41\text{ \%}[/tex]b)
[tex]\text{New value of the fund=1160+130}[/tex][tex]\text{New value of the fund= \$}1290[/tex][tex]\text{Percentage of original to the new value = }\frac{1290}{1160}\times100[/tex][tex]\text{Percentage of original to the new value =111.21 \%}[/tex]111.21% of the original value of the fund is the new value of the fund.
can you help me please
Help in writing an equation. I believe that it is supposed to be a linear equation
Since the information required us that the equation has to start in zero we can think of functions like the root of x but also we have to add a value of 1/3. In other words one equation with those characteristics is
[tex]y=\sqrt{x}+\frac{1}{3}[/tex]The area of this figure 20 in. is square inches. 28 in. 30 in. 7 in. 25 in.
The shape can be broken into two separate rectangles of the forms below.
Bothe shapes give a rectangle, therefore the area of the shape is
Area of Shape = Area of rectangle A + Area of rectangle B
Since Area of rectangle = LENGTH X BREADTH, we then have below
[tex]\begin{gathered} \text{Area of shape = (28 x 7)}+(25\times30) \\ =196+750 \\ =946\text{ square inches} \end{gathered}[/tex]In conclusion, the answer is 946 square inches
Type the correct answer in the box. Consider functions f and g: f(x) = (x+1)^3g(x)= x^1/3 +1Evaluate the function composition. (fog)(–64) =
The composition
[tex](f\circ g)(x)[/tex]Means that you have to evaluate x in g(x) first, and then evaluate that result in f(x)
In other words:
[tex](f\circ g)(x)=f(g(x))[/tex]Let's use this for this question:
[tex]\begin{gathered} f(x)=(x+1)^3 \\ g(x)=\sqrt[3]{x}+1 \\ \\ (f\circ g)(-64)=f(g(-64)) \\ \rightarrow g(-64)=-3 \\ \rightarrow f(-3)=-8 \\ \\ \text{Thereby} \\ (f\circ g)(-64)=-8 \end{gathered}[/tex]A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.
Who are the individuals on a data-set or on a study?The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.
In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.
Type of the pet.Age of the pet.Weight of the pet.Height of the pet.All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.
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what is the answer and how do i solve it?
EXPLANATION
Since we have the expression:
[tex]\frac{x}{x^2+x-6}-\frac{2}{x+3}[/tex]First, we need to find the least common multiplier as follows:
Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)
Ajust fractions based on the LCM:
[tex]=\frac{x}{\left(x-2\right)\left(x+3\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]\mathrm{Apply\: the\: fraction\: rule}\colon\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]=\frac{x-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]Expand\text{ x-2(x-2)}[/tex][tex]=\frac{-x+4}{\left(x-2\right)\left(x+3\right)}[/tex]The final expression is as follows:
[tex]=\frac{-x+4}{(x-2)(x+3)}[/tex]
By noon, the temperature in Nome had risen by 13 degrees. What was the temperature there at noon (Nome is -27 currently)
If there will be an increase of 13 degrees, the temperature will be -14 degrees.
What was the temperature there at noon?We know that by noon, the temperature had risen by 13 degrees, and currently the temperature is -27 degrees.
A "rise" in temperature means that the temperature increases, so the temperature at noon will be 13 degrees more than now, and now it is -27 degrees, so we will get:
-27° + 13° = -14°
The temperature at noon will be -14°.
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What is the area of a rectangle with vertices
(-1, -4), (-1, 6), (3, 6), and (3, -4)?
* 16 square units
24 square units
O 36 square units
40 square units
The most appropriate choice for distance formula will be given by Area of rectangle is 40 sq units
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Here,
Let A = (-1 , -4), B = (-1, 6), C = (3, 6) and D = (3, -4)
Length of AB =
[tex]\sqrt{((-1)-(-1))^2 + (-4-6)^2}\\\sqrt{100}\\10 units[/tex]
Length of BC =
[tex]\sqrt{((-1)-3)^2 + (6-6)^2}\\\sqrt{16}\\4 units[/tex]
Length of rectangle = 10 units
Breadth of rectangle = 4 units
Area of rectangle = [tex]10 \times 4[/tex] = 40 sq units
Fourth option is correct
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It's in the photo, it's a bit to hard to type out.
Perpendicular lines have slopes that are negative reciprocals.
If two perpendicular lines have slopes m1 and m2, then we have the following equation:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, we can analyze each pair.
a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.
b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.
c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.
d) In this case, the slopes are negative reciprocals:
[tex]-\frac{1}{m_2}=-\frac{1}{-\frac{3}{2}}=\frac{1}{\frac{3}{2}}=\frac{2}{3}=m_1[/tex]Then, this lines are perpendicular.
Answer: Option d.
For each expression build a rectangle using all of tiles,....
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]True or False? The end behaviors of each end of any quadratic function are always inthe same direction.
In general, given a quadratic function,
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ a,b,c\rightarrow\text{ constants} \end{gathered}[/tex]The end behaviors of each end of the function are given by the limits of f(x) when x approaches +/-infinite.
Therefore,
[tex]\lim_{x\to\infty}f(x)=\lim_{x\to\infty}ax^2=a\lim_{x\to\infty}x^2=a*\infty[/tex]and
[tex]\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}ax^2=a\lim_{x\to-\infty}x^2=a*\infty[/tex]Thus, the two limits are the same and depend on the sign of a.
Hence, the answer is True, the statement is True.Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
PLS HELP ASAP
Clara and Toby are telemarketers.
Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls.
If they continue at those rates, who will reach more people in 40 phone calls?
Use the drop-down menu to show your answer.
Which expression is undefined? (9-9) A 2 -3) )B. O C. )D. 0
Answer:
Option B
Step-by-step explanation:
Undefined expression:
An undefined expression is a division by 0, or a fraction in which the denominator is 0.
In this question, the undefined expression is given by option B.
Find an equation of the line described. Write the equation in slope-intercept form.With slope of -2 through (0,4)the equation of the line is y=0
y = -2x + 4
Explanations:The equation of the line having a slope m, and passing through the point (x₁, y₁) is given as:
y - y₁ = m (x - x₁)
From the description given:
The line passes through the point (0, 4)
That is, x₁ = 0, y₁ = 4
The slope of the line, m = -2
Substitute x₁ = 0, y₁ = 4, and m = -2 into the equation y - y₁ = m (x - x₁)
y - 4 = -2 (x - 0)
y - 4 = -2(x)
y - 4 = -2x
y = -2x + 4
A gumball machine contains orange, yellow, and purple gum balls. The probability of getting an orange gumball is 3/4. The probability of getting a yellow gumball is 1/6. If there are 36 gumballs in the machine, how many are there of each color number of purple marbles _______ number of yellow marbles_____ number of orange marbles______
Given:
Probability of getting orange gumball is, p(o) = 3/4.
Probability of getting yellow gumball is, p(y) = 1/6.
The objective is to find the number of each colored gumballs.
Since, the sum of the events of probability is always 1.
Then, the probability of purple ball p(p) can be calculated as,
[tex]\begin{gathered} \frac{3}{4}+\frac{1}{6}+p(p)=1 \\ p(p)=1-\frac{3}{4}-\frac{1}{6} \\ p(p)=\frac{12-3(3)-1(2)}{12} \\ p(p)=\frac{1}{12} \end{gathered}[/tex]Since, it is given that the total number of gumball is N = 36.
Then, the number of orange ball can be calculated as,
[tex]\begin{gathered} p(o)=\frac{n(o)}{N} \\ \frac{3}{4}=\frac{n(o)}{36} \\ n(o)=36\cdot\frac{3}{4} \\ n(o)=27\text{ balls.} \end{gathered}[/tex]Similarly, the number of yellow ball can be calculated as,
[tex]\begin{gathered} p(y)=\frac{n(y)}{N} \\ \frac{1}{6}=\frac{n(y)}{36} \\ n(y)=\frac{36}{6} \\ n(y)=6 \end{gathered}[/tex]And the number of purple ball can be calculated as,
[tex]\begin{gathered} p(p)=\frac{n(p)_{}}{N} \\ \frac{1}{12}=\frac{n(p)}{36} \\ n(p)=\frac{36}{12} \\ n(p)=3 \end{gathered}[/tex]Hence, the number of orange ball is 27, number yellow ball is 6 and number of purple ball is 3.
If Allie’s parents are willing to spend $300 for a party, how many people can attend?
At least 20 people can attend the party
Dave and his friends went out to celebrate his birthday at Chill's in buda. their meal cost $86 and they left a 15% tip how much was the total bill including tip?
The meal cost is $86
its 15% is:
$86 x 0.15 = $12.9
then the tip was $12.9. Then, the total bill would be:
$86 + $12.9 = $98.9
that is the total bill was $98.9
HELP PLEASEEEEE!!!!!!
Answer: D=2/7 R=4/7
Step-by-step explanation: there are 7 parts and D is the 2nd part R is the 4th part.
y = 2x divided by 6?
Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y
Step-by-step explanation: